Algebraic and Geometric Methods in Enumerative Combinatorics
by Federico Ardila
Publisher: arXiv 2014
Number of pages: 143
The guiding principle was to focus on algebraic and geometric techniques that are useful towards the solution of enumerative problems. The main goal of this survey is to state clearly and concisely some of the most useful tools in algebraic and geometric enumeration, and to give many examples that quickly and concretely illustrate how to put these tools to use.
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by S. E. Payne - University of Colorado
These notes deal with enumerative combinatorics. The author included some traditional material and some truly nontrivial material, albeit with a treatment that makes it accessible to the student. He derives a variety of techniques for counting.
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Contents: Uniform Distribution; Classical Discrepancy Problem; Generalization of the Problem; Introduction to Lower Bounds; Introduction to Upper Bounds; Fourier Transform Techniques; Upper Bounds in the Classical Problem; Disc Segment Problem; etc.
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This introduction to combinatorics, the interaction between computer science and mathematics, is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. Some ability to construct proofs is assumed.
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Contents: Subsets and binomial coefficients; Selections and arrangements; Power series; Recurrence relations; Partitions and permutations; The Principle of Inclusion and Exclusion; Families of sets; Systems of distinct representatives; etc.